It seem like you can slice it so that you get a mirroring hyperbola using this one cone. I doubt if we can get a parabola slicing from this surface. Because although this cone has their slanted height, the other side is "open", and slicing along the slanted height would result in two separate segments. Similarly, I don't think we can slice a circle from this surface.
Patrick mentioned that cubic curve should also show up, but I haven't figure out how can I get it. I wonder if I need a cone with more than 720 degree to generate cubic slice. And it will be fun to look into how the set of curve resulted from slicing a cone changes as we increase the angle to (720, 1080), (1080, 1440), and so on.
I wonder if there is an equation to represent this surface (if there is one, then I can construct the surface with GeoGebra and play with it). I tried to google it but I couldn't catch much information related to this topic.
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To address some other stuff we did today. There's two things I found fascinating. One of them is the construction of parabola using a focus point and a line. Especially since this definition of parabola appears in BC curriculum, it would be easy to bring this activity into the classroom.
The other thing was the star blanket we saw from the video, particularly the seven point one. I googled it later, but the vast majority I showed up was eight point.
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